# Improved Bounds on Sidon Sets via Lattice Packings of Simplices

arXiv: https://arxiv.org/abs/1610.01341 · HTML: https://mlsanity.com/paper/1610.01341/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Oct 2016.

## Built on by (most cited first, 1 of 1)

- [Federated Classification in Hyperbolic Spaces via Secure Aggregation of Convex Hulls](https://mlsanity.com/paper/2308.06895/) (2023)

## Abstract (arXiv)

A  Bh  set (or Sidon set of order  h ) in an Abelian group  G  is any subset  b0, b1, ldots,bn  of  G  with the property that all the sums  bi1 + cdots + bih  are different up to the order of the summands. Let  φ(h,n)  denote the order of the smallest Abelian group containing a  Bh  set of cardinality  n + 1 . It is shown that [ limh → ∞ frac φ(h,n)  hn  = frac1n! δL(trianglen) , ] where  δL(trianglen)  is the lattice packing density of an  n -simplex in Euclidean space. This determines the asymptotics exactly in cases where this density is known ( n ≤ 3 ) and gives improved bounds on  φ(h,n)  in the remaining cases. The corresponding geometric characterization of bases of order  h  in finite Abelian groups in terms of lattice coverings by simplices is also given.